Sensors, systems and methods for compensating for thermal EMF

ABSTRACT

Embodiments relate to sensor systems and methods that can compensate for thermal EMF effects that can cause residual offset and other errors in sensor systems. In one embodiment, a sensor system comprises at least one temperature sensor arranged proximate a primary sensor element, e.g., a Hall plate in an embodiment in which the sensor system comprises a Hall-effect magnetic field sensing system, though other types of magnetic field and sensors more generally can be used in other embodiments. In another embodiment, a plurality of temperature sensors can be used, with each one arranged proximate a different sensor contact or element. In an example in which the Hall plate is operated according to a spinning operation scheme, the at least one temperature sensor can be configured to sense a temperature in each operating phase, and the individual sensed temperatures can be combined and used to provide a temperature-dependent compensation signal.

TECHNICAL FIELD

The invention relates generally to sensors and more particularly tosensors, systems and methods which compensate for effects of thermalelectromotive force (EMF).

BACKGROUND

Sensors can be affected by many different internal and externalcharacteristics that can make the sensor output signals less accurate.One of these characteristics is thermal electromotive force (EMF), whichrelates to the effects temperature can have on the movement of electriccharge in a material. A temperature gradient in a material, for example,can affect charge flow in the material much like an applied electricfield, by pushing charges in a particular direction. This can beamplified in the presence of electric or magnetic fields, orconcentration gradients. Thermal EMFs also can cause temperature-relatedcharges in two primary situations: first, an inhomogeneous temperature(i.e., a temperature gradient) in a homogeneous material, or ahomogeneous temperature in an inhomogeneous material. The second canoccur, e.g., at device contacts, with the voltage referred to as athermal contact voltage. Both are undesirable with respect to sensoroperation and output signal accuracy.

There are many different ways in which temperature can influence charge,only some of which are related to thermal EMF. For example, magneticsensitivity in Hall effect devices and resistivity changes due totemperature generally are not related to any thermal EMF effects andtherefore may not be addressed or compensated for by embodimentsdiscussed herein. Sensor output signals, particularly when the sensorsoperate according to spinning current or voltage schemes, however, canbe affected by thermal EMF. In one example, a sensor system comprisesHall plates which are operated in sequential operating phases. Differentterminals of the Hall plates are tapped as supply and output terminalsin each operating phase, such that the current flow direction or spatialdistribution of current is different from phase to phase. A spinningoutput signal can be obtained by combining the signals from theindividual operating phases. Hall plates, in fact magnetic field sensorsin general, can experience offset errors which result in an outputsignal when there is no applied magnetic field. Offset errors in eachoperating phase can be largely canceled in spinning schemes due to thecombination of the individual operating phase signals, such that littleor no residual offset remains in the combined output signal.

Unfortunately, residual offset errors often remain, such that somespinning scheme sensor systems provide residual offset compensation.Referring to FIG. 1, such systems typically comprise a temperaturesensor arranged in close proximity to the Hall plate because offsetcorrection usually is not constant over temperature. The systemtherefore can sense the temperature, determine a compensation signalbased on the temperature, and take this compensation signal into accountin the spinning output signal. Thus, this conventional approach combinesthe phase temperature signals only by averaging, which can be consideredequivalent to an implicit low-pass filtering of a slow temperaturesensor. A challenge, however, is determining the compensation signal.Because the residual offset of spinning Hall schemes is stochastic, itdepends on the actual individual device, and the temperature of thisdevice, and it can change during the operational lifetime of the device.Thus, even if individual device calibration could be performedefficiently and effectively during end-of-line testing, changes over thelifetime of the device can reduce the accuracy of the calibration andresult in thermal EMF-related residual offset errors.

Conventional solutions presume that thermal EMF effects are canceledthrough use of polarity inversion in sequential operating phases (i.e.,only the polarity of the supply changes) and a spinning voltage ratherthan current technique. This may not be the case, however, because inpractice the temperature distribution can change when the polarity ofthe supply voltage is inverted.

SUMMARY

Embodiments relate to sensors, systems and methods for estimating and/orreducing residual offset errors related to thermal electromotive force(EMF).

In an embodiment, a sensor system comprises a first sensor elementarranged on a substrate and configured to sense a physical quantity inat least one operating phase; a second sensor element arranged thermallyproximate the first sensor element on the substrate and configured tosense a spatial gradient of temperature within the first sensor elementduring at least a portion of the at least one operating phase; andcircuitry coupled to the first sensor element and the second sensorelement and configured to combine a signal of the first sensor elementrelated to the sensed physical quantity with a signal of the secondsensor element related to the sensed spatial gradient of temperaturesampled during the same portion of the at least one operating phase toobtain an output signal indicative of the physical quantity.

In an embodiment, a sensor configured to sense a physical quantitycomprises a first electrically conducting region of a substratecomprising a first contact; a first terminal coupled to the firstcontact and comprising a material having a first effective Seebeckcoefficient; a second terminal coupled to the first contact andcomprising a material having a second effective Seebeck coefficient; andcircuitry selectively coupled to the first and second terminals to tapfirst and second signals and combine the first and second signals.

In an embodiment, a device comprises an output signal contact coupled toa first wire and to a second wire; and a reference contact coupled to athird wire and to a fourth wire, wherein a difference in an effectiveSeebeck coefficient between the first wire and the second wire issubstantially the same as a difference in an effective Seebeckcoefficient between the third wire and the fourth wire.

In an embodiment, a method comprises obtaining a first signal by sensinga first physical quantity in at least one operating phase by a firstsensor; obtaining a second signal by sensing a spatial gradient oftemperature of the first sensor during a portion of the at least oneoperating phase when the first physical quantity is sensed; and reducingan offset error in the first signal by combining the first and secondsignals from the at least one operating phase.

In an embodiment, a method comprises obtaining a first set of signals ina plurality of operating phases by sensing a magnetic field at a set ofcontacts tapped by a first set of terminals having a first effectiveSeebeck coefficient; obtaining a second set of signals in the pluralityof operating phases by sensing a magnetic field at the set of contactstapped by a second set of terminals having a second effective Seebeckcoefficient different from the first effective Seebeck coefficient; andcombining the first and second sets of signals.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be more completely understood in consideration of thefollowing detailed description of various embodiments of the inventionin connection with the accompanying drawings, in which:

FIG. 1 is a block diagram of a sensor system.

FIG. 2A is a diagram of a Hall plate according to an embodiment.

FIG. 2B is a diagram of a vertical Hall sensor device according to anembodiment.

FIG. 2C is a diagram of a Hall plate according to an embodiment.

FIG. 2D is a perspective view of a potential distribution in a Hallplate during an operating phase according to an embodiment.

FIG. 2E is a coupling arrangement of a Hall plate in a first operatingphase according to an embodiment.

FIG. 2F is a coupling arrangement of a Hall plate in a second operatingphase according to an embodiment.

FIG. 2G is a coupling arrangement of a Hall plate in a third operatingphase according to an embodiment.

FIG. 2H is a coupling arrangement of a Hall plate in a fourth operatingphase according to an embodiment.

FIG. 2I is a block diagram of a sensor system according to anembodiment.

FIG. 3 is a side cross-sectional view of an arrangement of first andsecond sensor devices according to an embodiment.

FIG. 4A is a diagram of a sensor coupling arrangement according to anembodiment.

FIG. 4B is a diagram of a sensor coupling arrangement according to anembodiment.

FIG. 5A is a block diagram of a sensor system according to anembodiment.

FIG. 5B is a block diagram of a sensor system according to anembodiment.

FIG. 6A is a diagram of another coupling arrangement according to anembodiment.

FIG. 6B is a block diagram of another sensor system according to anembodiment.

FIG. 6C is a block diagram of another sensor system according to anembodiment.

FIG. 7A is a diagram of a coupling arrangement of a Hall plate accordingto an embodiment.

FIG. 7B is a diagram of a coupling arrangement of a Hall plate accordingto an embodiment.

FIG. 7C is a diagram of a coupling arrangement of a Hall plate systemaccording to an embodiment.

FIG. 7D is a diagram of a coupling arrangement of a Hall plate in twooperating phases of a spinning current scheme according to anembodiment.

FIG. 7E is a diagram of a coupling arrangement of a Hall plate in twooperating phases of a spinning current scheme according to anembodiment.

FIG. 8A is a depiction of a temperature distribution in a Hall plateaccording to an embodiment.

FIG. 8B is a depiction of transient temperature behavior of a Hall platein a spinning current scheme according to an embodiment.

FIG. 9 is a side cross-sectional view of an arrangement of a sensordevice according to an embodiment.

While the invention is amenable to various modifications and alternativeforms, specifics thereof have been shown by way of example in thedrawings and will be described in detail. It should be understood,however, that the intention is not to limit the invention to theparticular embodiments described. On the contrary, the intention is tocover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention as defined by the appended claims.

DETAILED DESCRIPTION

Embodiments relate to sensor systems and methods that can compensate forthermal EMF effects that can cause residual offset and other errors insensor systems. In one embodiment, a sensor system comprises at leastone temperature or temperature gradient sensor arranged proximate afirst sensor element configured to sense a physical quantity, such as amagnetic field, temperature, pressure, force, mechanical stress, or someother physical quantity. For example, the first sensor elementcomprises, e.g., a Hall plate in an embodiment in which the sensorsystem comprises a Hall-effect magnetic field sensing system, thoughother types of magnetic field sensors, and sensors more generally, canbe used as the first sensor in other embodiments. In another embodiment,a plurality of temperature sensors can be used, with each one arrangedproximate a different sensor contact or element. In an example in whichthe Hall plate is operated according to a spinning operation scheme, theat least one temperature sensor can be configured to sense a temperaturein each operating phase, and the individual sensed temperatures can becombined and used to provide a temperature-dependent compensationsignal.

Thermal EMF, the characteristic for which embodiments aim to compensate,can be quantified by the Seebeck coefficient for any particularmaterial. For n-doped silicon with a concentration of about 10^16/cm³,which is typical for the active region of Hall effect devices discussedherein in some embodiments, the Seebeck coefficient is about −1,200 μV/°C. at room temperature. N-doped poly-silicon with a resistivity of about7 milli-Ohms*cm has a Seebeck coefficient of about 200 μV/° C., andn-doped poly-silicon with a resistivity of about 0.8 milli-Ohms*cm has aSeebeck coefficient of about 80 μV/° C. Aluminum, often used for metalinterconnect lines in integrated circuit technologies, has a negligibleSeebeck coefficient, only about −0.5 μV/° C. These Seebeck coefficientsare representative examples of materials which could be suitable for usein embodiments, but this list is not exhaustive, nor is it limiting withrespect to materials which can or may be used, as appreciated by thoseskilled in the art. Additionally, the Seebeck coefficient is notcritical, and embodiments are related to reducing or eliminating theunderlying thermal EMF.

Embodiments relate to situations in which output signals are tapped atterminals, which can be subject to small additive voltages caused bythermal EMF. In most cases the signals are tapped between two terminalswhich are at different temperatures, and therefore the tapped signal hasa small additive part that is proportional to the temperature differencebetween the terminals. In other cases the signals can be tapped betweena terminal and a reference terminal, such as, e.g., one that is atground potential. Here again the terminal and the reference terminal canhave different temperatures which can cause small superimposed additivethermo-EMF signals. In still other cases a signal can be tapped at thesame contact at different times (e.g., in different operating phases),with multiple sampled values then combined to provide an overall signal.If the temperature at the contact changes over time, a small additivethermo-EMF can be superimposed on the signals. It should be kept in mindthat the different temperatures at the terminals do not affect theisothermal signal (i.e., the signal if the terminals were at identicaltemperatures), so the isothermal signal is not multiplied by some factorthat depends on the temperature difference. Instead, the signal tappedbetween terminals at different temperatures is equal to the isothermalsignal plus a small additive thermo-EMF contribution, which isproportional to the temperature difference between the terminals. It isthis thermo-EMF contribution which embodiments aim to address.

Referring to FIG. 2A, a simplified diagram of a Hall plate 202 isdepicted. The particular depiction in FIG. 2 is not to scale. Thediagram of FIG. 2, as well as others which may be used herein, are forexample and illustrative purposes and are complemented by thisdiscussion, the other figures and this entire application as a whole.Some figures can include block diagrams, wherein the blocks canrepresent physical objects, functions, concepts and/or combinationsthereof. Moreover, while some embodiments discussed herein refer tomagnetic field sensors, including Hall and vertical Hall devices, othersensors can be used in other embodiments, and the use and depiction ofHall plate 202 in this embodiment is not to be considered limiting.

Hall plate 202 comprises three contacts 204 a, 204 b and 204 c. Inembodiments, Hall plate 202 can be operated in a spinning scheme, inwhich contacts 204 a, 204 b, 204 c can be differently coupled as supplyand signal contacts in different operating phases. As previouslymentioned, in a spinning current or voltage scheme, different contactsof Hall plate 202 are coupled in each sequential operating phase suchthat the current flow direction or spatial distribution of current inHall plate 202 is different from one operating phase to the next. Thenumber of contacts and the number of operating phases can vary inembodiments.

While FIG. 2A depicts a single Hall plate 202, in other embodiments, thesensor can comprise a plurality of Hall plates 202 differently coupledwith one another in a similar manner in different operating phases. FIG.2B depicts one example of a vertical Hall device 212 comprising threecontacts 214 a, 214 b and 214 c and which can be operated similarly toHall plate 202 except that vertical Hall device 212 is sensitive to adifferent magnetic field component than Hall plate 202, as appreciatedby those skilled in the art. FIG. 2C depicts an example octagonal Hallplate 202 comprising four contacts or contact diffusions 204 a, 204 b,204 c, 204 d. As previously mentioned, the size, shape, configurationand number of contacts, among other characteristics, can vary inembodiments, and Hall plate 202 will be used generally herein to referto a Hall plate without limit with respect to the embodiments of FIGS.2A, 2C or other Hall plates depicted, vertical Hall device 212 of FIG.2B, or other particular characteristics which can vary from embodimentto embodiment. Hall plate 202 comprises an active region 226 and aboundary or isolation of active region 226 at perimeter 227. FIG. 2Ddepicts an example potential distribution within Hall plate 202 inoperation. The distribution of potential within Hall plate 202 leads todistribution of temperatures within Hall plate 202, or a spatialdistribution of temperature. The effects of thermal EMF can influencethe distribution of potential within Hall plate 202, and therefore alsothe spatial distribution of temperature therein.

In one embodiment, at least one temperature sensor can be arrangedproximate Hall plate 202. For example, Hall plate 202 can be arranged ona semiconductor substrate, and a temperature sensor can be arranged inclose physical proximity to one or more contacts 204 a, 204 b, 204 c, toHall plate 202 generally, or another relevant portion of Hall plate 202.In one embodiment, a single temperature sensor is used, and that singletemperature sensor is configured to sense temperatures in Hall plate 202associated with the different power dissipations that can occur in Hallplate 202 in different operating phases of the spinning scheme. Fromthese measurements, system 100 can estimate thermal EMF changes orfluctuations from phase-to-phase. In another embodiment, the temperaturesensor comprises a plurality of temperature sensor elements, for exampleone associated with each contact of Hall plate 202, one positionedbetween each adjacent contact of Hall plate 202, and/or one comprising aplurality of wires or terminals coupled to or with Hall plate 202 suchthat a spatial distribution of temperature in Hall plate 202 can besensed. In essence, however, at least one temperature sensor aims tosense and measure thermal EMF mismatches between different contacts,e.g., two contacts being used in a differential measurement, in Hallplate 202.

The temperature sensor can also be used in embodiments comprising singleoutput voltages or currents, in contrast to differential outputs. Inthese embodiments, the total thermal EMF contributes to the outputsignal at an output contact. One example can be vertical Hall device 212of FIG. 2B, in which current flows between two contacts and an outputsignal is a potential measured at the third contact. Thus, regardless ofwhether the particular sensor implemented is operated in a single phaseor according to a multi-phase spinning current or voltage scheme, thethermal EMF at each output or signal terminal in each operating phase isrelevant to the compensation effort. Vertical Hall device 212 also canbe used in spinning schemes in other embodiments.

The temperature sensor can be sampled during sampling of Hall plate 202in embodiments, such that an instantaneous temperature can be obtained.In one example, operating phases of a sensor device comprising Hallplate 202 are at least about 1 micro-second (μs) long, for example about2 μs, and a temperature sensor that can keep pace and sample signals atappropriate time intervals is needed. In embodiments, therefore, thetemperature sensor is one which has a low thermal mass and heatretention. The temperature sensor also can have a high bandwidth inembodiments. For example, if the Hall sensor 202 is operated in aspinning current scheme at 500 kHz, a suitable bandwidth can be about 1MHz. It is also advantageous in embodiments for the temperature sensorto have a high spatial resolution in order to detect spatial gradientsof temperature in Hall plate 202. In embodiments, the spatial resolutionof the temperature sensor is at least about 10 micrometers (μm), forexample about 1 μm. Additionally, however, the temperature sensor can berelatively simple in embodiments, to avoid adding complexity and expenseto the overall sensor system given that it, and the underlying goal ofthermal EMF compensation, can be an add-on feature in various sensorsystems and implementations. The temperature sensor also should notintroduce or increase parasitic effects, such as high temperatureleakage currents or stray capacitances, particularly those which couldhave an effect on the Hall sensor. Thus, temperature sensors whichrequire too much power, highly sophisticated signal processing, a largearea, or other features which can raise their cost or need for resourceswithin a sensor system can be less suitable in most embodiments butcould still have applicability in certain specialized applications.

Whether the temperature sensor comprises a single temperature sensorelement or a plurality thereof, and whether the temperature sensor isimplemented according to the embodiments of FIG. 3, FIG. 4 or some otherembodiment discussed herein below, the temperature sensor can operate ineach operating phase of a spinning scheme of Hall plate 202 or anothersensor device. In other embodiments, the temperature sensor need notoperate in every phase. The various individual phase temperature signalsfrom the temperature sensor can be combined, while the individual phasesignals from Hall plate 202 also can be combined, by the same ordifferent circuitry, on-chip or off. A temperature signal and a spinningoutput signal can be determined, with the temperature signal used todetermine a temperature-dependent offset correction signal, which can becombined with the spinning output signal to provide an overall systemoutput signal.

For example, and referring to FIG. 2I, a spatial gradient temperaturesensor 230 can be arranged thermally proximate another sensor element232, which can comprise a spinning Hall sensor or some other sensor invarious embodiments, on a substrate 234. Sensor 230 is configured tosense a spatial gradient of temperature within sensor element 232 duringat least a portion of at least one operating phase. For example, sensor232 can be operated in a plurality of operating phases according to aspinning scheme in one embodiment. Circuitry 236, which can be arrangedon or off of substrate 234 in embodiments, is coupled to sensors 230 and232 and can be configured to combine signals of sensor 232 related to asensed physical quantity (e.g., a magnetic field) in each of at leastone operating phases, and to combine signals from sensor 230 related toa sensed spatial gradient of temperature in sensor 232 sampled duringthe same portion of the at least one operating phase. Those signals canthen be combined to obtain an overall output signal indicative of thephysical quantity. Using the combined signals from sensor 230, an offsetcorrection can be determined and used in the combining to obtain theoverall output signal, whereby that overall output signal is correctedfor an offset related to thermal EMF.

Turning to specific example embodiments of a temperature and/or spatialgradient temperature sensor, in one example implementation the sensorcomprises a pn-junction. Pn-junctions are often used to measuretemperature on semiconductor substrates and thus can be suitable invarious embodiments. Pn-junctions also have the advantage of beingrelatively easily arranged in close proximity to the contacts of, e.g,Hall plate 202. One example embodiment of a temperature sensor 104comprising a pn-junction is depicted in FIG. 3. Temperature sensor 104is arranged proximate a Hall plate 202, in particular contact 204 a,spaced apart on a substrate 302 by a distance d with optional galvanicisolation. In other embodiments, temperature sensor 104 and Hall plate202 can be electrically coupled, though this would have an effect on theperformance of one or both of Hall plate 202 and sensor 104 andtherefore may not be suitable in all implementations.

Temperature sensor 104 comprises an n-tub 304 and a p-tub 306, thoughthese can be reversed in other embodiments, and is biased by a constantcurrent source 308. The voltage across current source 308 is a strongfunction of temperature and thus can be used as a temperature sensor.Additional components not specifically depicted, including signalconditioning circuitry components like precision amplifiers andanalog-to-digital converters (ADC) can be included in variousembodiments.

An alternative implementation to that depicted in FIG. 3 is depicted inFIG. 4. Here, temperature sensing is integrated with a Hall or othersensor or type of device by providing additional contacts, terminals,wires, and/or other elements to sense temperatures and/or spatialgradients of temperature in Hall plate 202. The temperature sensing ofthe embodiment of FIG. 4 can be simpler than that of FIG. 3 and candetermine the temperature or a temperature gradient at or withincontacts of Hall plate 202 based on thermal voltage differences betweendifferent materials.

In FIG. 4A, two terminals 204 a and 204 b of a Hall plate 202 (e.g., asdepicted in FIG. 2C or another figure, or having some otherconfiguration whether explicitly depicted or not herein) are shown.Terminals 204 a and 204 b can comprise wires, metal lines or some othersuitable configuration in embodiments. In general, a terminal or a wirecan be a device, circuit or circuit component with a resistance that isless than about ten times a signal output resistance of a sensor deviceat the respective contact which the terminal or wire taps, though thiscan vary in embodiments. It can be advantageous in embodiments to havewires or terminals with a low resistance and low parasitics. Terminals204 a and 204 b, as well as terminals 410 a and 410 b, generally are atthe same temperature T′. Though not depicted in FIG. 4A, terminals 204 aand 240 b can be coupled (e.g., via one or a stack of tungsten plugs) totransistor pairs in a signal amplifier or other circuitry, also arrangedisothermally.

The circuitry and elements of FIG. 4A can be arranged relative to one ormore contacts of a Hall plate or other device, and the Hall plate cancomprise a low-doped n-region in one embodiment, or some otherconfiguration or composition in other embodiments. Terminals 204 a and204 b are each coupled by plugs 402 to an interconnect line 404 a and404 b, respectively, which can be arranged between inter-metal oxidelayers in or on substrate 400. In embodiments, plugs 402 can comprisetungsten-filled holes which have been etched or otherwise formed ininter-metal oxide layers of substrate 400, though other materials,configurations and methods of formation can be used in otherembodiments. Interconnect lines 404 a and 404 b can comprise lines,wires or other suitable structures and couple contacts 204 a and 204 bof the sensor with contact diffusions 406 a and 406 b, respectively, viavarious additional plugs 403 a, 403 b, which can be the same as ordifferent from each other and/or plugs 402 in embodiments. In oneembodiment, contact diffusions 406 a and 406 b comprise shallow n+S/Dcontact diffusions formed in regions 408 a and 408 b. Contact diffusions406 a and 406 b each are coupled to terminals 410 a and 410 b via plugs403 a and 403 b, respectively, and each can comprise an output contactof the sensor for providing a signal related to the physical quantitysensed by the sensor, or a reference point to be used in sensing atemperature difference between two points.

In embodiments, terminals 410 a and 410 b can comprise wires, metallines or other suitable materials or structures. In general, elements204 a, 204 b, 404 a, 404 b, 410 a and 410 b depicted in FIG. 4A each canbe considered to be wires, terminals, interconnects or some otherstructure, including in different contexts given that the figure is apartial representation and merely exemplary, though different terms(e.g., interconnect lines vs. terminals and/or wires) may be used hereinfor purposes of example and illustration. What can be of more interestin embodiments is the Seebeck coefficient of and/or material which thoseelements 204 a, 204 b, 404 a, 404 b, 410 a and 410 b comprise,particularly when considered relative to one another and with respect towhere (i.e., between which terminals and/or wires, and/or betweencontacts) signals are tapped or otherwise considered in variousembodiments.

For example, in embodiments, interconnect lines 404 a and 404 b comprisea different material and/or have a different Seebeck coefficient thanterminals 410 a, 410 b. In one embodiment, interconnect lines 404 a and404 b comprise a semiconductor material, such as polysilicon, silicon,germanium, a single-crystal semiconductor material or a poly-crystallinesemiconductor material, though other materials can be used in otherembodiments, such that the material of interconnect lines 404 a and 404b has a different contact voltage than the material of terminals 410 a,410 b. In another embodiment, the materials can be selected to maximizea difference in Seebeck coefficients therebetween. Thus, there can be adifference in thermal EMF between the materials which can be sensed atterminals 410 a and 410 b, and at terminals 204 a and 204 b, and used tomeasure the thermal EMF. Herein throughout, an example in whichinterconnects 404 a and 404 b comprise polysilicon and terminals 410 aand 410 b comprise a metal generally will be used, though this exampleis not be to limiting with respect to other embodiments. The potentialtherefore can be tapped at the ends of terminals 410 a and 410 b, butalso at terminals 204 a and 204 b, such that the terminals 204 a and 204b can be used to measure a differential signal that can be compared witha differential signal at terminals 410 a and 410 b, which should differfrom one another by the thermal contact voltages between the polysiliconof interconnect lines 404 a and 404 b and the metal of interconnectlines 410 a and 410 b.

In other words, a signal measured between terminals 410 a and 410 b caninclude some unknown thermal EMF contribution caused at least in part bydifferent temperatures T1, T2 of contacts 406 a, 406 b, respectively,and a signal measured between terminals 204 a and 204 b can include thesame unknown thermal EMF contribution in addition to a contribution frompolysilicon interconnect lines 404 a and 404 b. There is a strongcorrelation between the additional polysilicon contribution and theunknown thermal EMF contribution, because they are proportional to thetemperature difference T1−T2 of contacts 406 a and 406 b. Hence, thefollowing can be used:V(C1′)−V(C2′)=F[B]+Off′ and V(C1″)−V(C2″)=F[B]+Off″where F[B] is a function of the magnetic field, with F[0]=0, andOff″=Off′+k(T1−T2), with k being a difference in the Seebeck coefficientof the materials of terminals 410 a and 410 b and interconnect lines 404a and 404 b. C1′ represents terminal 410 a, C2′ represents terminal 410b, C1″ represents terminal 204 a and C2″ represents terminal 204 b inone operating phase, though the coupling arrangements will change fromone operating phase to the next. Referring specifically to FIG. 4:V(204a)−V(204b)=k(404a)*(T1−T′)+k(408)*(T2−T1)+V(408ab)+k(404b)*(T′−T2)V(410a)−V(410b)=k(410a)*(T1−T′)+k(408)*(T2−T1)+V(408ab)+k(410b)*(T′−T2)→V(204a)−V(204b)−(V(410a)−V(410b))==(k(404a)−k(410a))*(T1−T′)+(k(404b)−k(410b))*(T′−T2)An assumption here is that conductive regions 408 a and 408 b have aneffective Seebeck coefficient k(408) and that at isothermal conditions(T1=T2) a voltage V(408 ab) (e.g., an output voltage of a Hall effectdevice) is present between regions 408 a and 408 b tapped at, e.g.,contact diffusions 406 a and 406 b. This assumes that a difference inthe effective Seebeck coefficients between wire or interconnect 404 aand wire or terminal 410 a is the same as the difference in theeffective Seebeck coefficients between interconnect 404 b and wire orterminal 410 b. This can be addressed in embodiments, as discussedherein above, by interconnects 404 a and 404 b comprising the samematerial, and wires or terminals 410 a and 410 b comprising the samematerial. Note that it is the “effective” Seebeck coefficient which isof interest because an individual Seebeck coefficient of one portion ormaterial could be the same. The effective Seebeck coefficients of otherparts or portions of the sensor system are generally irrelevant, so longas the parts or portions are generally at a homogeneous temperature. Forexample, in FIG. 4A the effective Seebeck coefficients of plugs 402comprising tungsten are irrelevant, because there are no spatialtemperature gradients within each of them. Therefore, it makes nodifference if terminal 410 a is coupled to contact diffusion 406 adirectly or via a single tungsten plug or via a stack of two or moretungsten plugs, as long as each tungsten plug has no significanttemperature difference within its body. Thus, in FIG. 4A it would alsobe possible to have a first tungsten plug between contact 406 a and wire404 a and to have a stack of two further tungsten plugs between contact406 a and terminal 410 a such that there is no direct contact betweenthe stack of the two further tungsten plugs and wire 404 a. In practice,a large number of tungsten plugs may be used between contact diffusion406 a and wire 404 a or wire 410 a, all of them electrically connectedin parallel. Since the contact diffusions have finite size, space fortungsten plugs is limited there, and so one is usually inclined to stacklayers, each layer having a large number of parallel connected plugs, asshown in FIG. 4A exemplarily for a single plug per layer. Thus,V(204a)−V(204b)−(V(410a)−V(410b))=(k(404a)−k(410a))*(T1−T2)This enables a measurement of temperature difference T1−T2 if theSeebeck coefficients as mentioned above (e.g., between wire orinterconnect 404 a and wire or terminal 410 a, and between interconnect404 b and wire or terminal 410 b) are different.

The offset of the first sensor (e.g., the Hall effect device) comprisesa raw offset Off and a thermoelectric contribution Off_(therm) accordingto Off′=Off+Off_(therm). The thermoelectric contribution Off_(therm) hasa strong correlation with the temperature difference T1−T2.

While this is valid for a single operating phase, in a spinning schemeHall plate 202 is operated in several phases, and a total signal iscomputed as a sum over all individual phases:S′=Σ(V(C ₁′)−V(C ₂′))=Σ(F[B]+Off′)=Σ(F[B]+Off+Off_(therm))measured at terminals 410 a and 410 b, andS″=Σ(V(C ₁″)−V(C ₂″)=Σ(F[B]+Off″)=Σ(F[B]+Off+k(T ₁ −T ₂)+Off_(therm))measured at terminals 204 a and 204 b, with the indices changingaccording to the operating phases. The difference can then be computedby the sensor system:S″−S′=Σk(T ₁ −T ₂)

Due to the strong correlation, this difference can be used to estimatethe residual offset ΣOff_(therm). One way to obtain this estimation isby a multiplication with a predefined factor x:ΣOff_(therm) ≅xΣk(T ₁ −T ₂)This factor x can depend on the technology and the geometry of the Hallsensor, as well as on the temperature, operating frequency, electricbiasing and any mechanical stress acting on the sensor. In embodiments,x can be determined based on characterization of sensor devices in thelaboratory or manufacturing-level testing. Once ΣOff_(therm) isdetermined, it can be subtracted from S′ to get a signal without offsetdue to thermo-EMF. Due to spinning Hall schemes, the purely resistiveoffset (i.e., the one which can be described by an asymmetric Wheatstonebridge circuit in an equivalent circuit diagram) vanishes, ΣOff=0, sothat S′−ΣOff_(therm)=S′−x(S″−S′)==(1+x)S′−xS″ is void of any offset.

A simple way, therefore, to measure a temperature difference betweencontact diffusions 406 a and 406 b can be as follows, where T1 is thetemperature at contact diffusion 406 a and T2 is the temperature atcontact diffusion 406 b:T1−T2=(1/k)*(V(204a)−V(204b)−(V(410a)−V(410b)))where k is the difference in the Seebeck coefficients of the metal lines(e.g., terminals 410 a and 410 b) and the polysilicon lines (e.g.,interconnects 404 a and 404 b). This can be efficiently implemented inembodiments because V(410 a)−V(410 b) and V(204 a)−V(204 b) are alreadymeasured by signal conditioning circuitry of the sensor. Dedicatedhardware, such as preamplifiers and ADCs, therefore are not needed tomeasure T1−T2 in embodiments. In another embodiment, T1−T′ can beobtained by determining V(410 a)−V(204 a), and T2−T′ by V(410 b)−V(204b), though dedicated preamplifiers not otherwise needed by the sensorcan be necessary.

Thus, a sensor system can be depicted as system 500 as in FIG. 5A,comprising Hall plate 202. As mentioned elsewhere herein, Hall plate 202of FIG. 5A, or any other figure (e.g., FIG. 6, FIG. 7, etc.) orembodiment whether explicitly depicted or not, can be as depicted in oneof the figures (e.g., FIG. 2A or 2C), having some other configurationnot explicitly depicted, or comprise a vertical Hall device (e.g., Halldevice 212 of FIG. 2B or having some other configuration not explicitlydepicted here). The output signals are tapped at contact diffusions 406a and 406 b by elements (e.g., terminals 204 a, 204 b, 410 a, 410 b andinterconnect lines 404 a and 404 b) forming two different materialpairings which have different Seebeck coefficients as discussed above toobtain a first set of phase signals (e.g., terminals 410 a and 410 b,comprising metal, for example) and a second set of phase signals (e.g.,interconnect lines 404 a and 404 b, comprising semiconductor material,for example, and tapped via terminals 204 a and 204 b). The signals fromall phases are then combined at circuitry blocks 506 and 508, and adifference between the combined signal is determined at block 510. In anembodiment, blocks 506 and 508 can be combined and time-multiplexed,with metal or polysilicon phase signals sampled in any particular phaseand then stored in a memory until combined at block 510. The output ofblock 510 is a measure of temperature asymmetries in the sensor duringthe various operating phases and/or temperature fluctuations of thecontacts (e.g., contacts 204 a, 204 b) during the various operatingphases. It may be equal to S″−S′=Σk(T₁−T₂). In embodiments, this shouldcorrelate with the residual offset.

This difference, the output of block 510, is then used to estimate theresidual offset at block 512. Its output may be equal to xΣk(T₁−T₂).This estimated residual offset is then subtracted from the spinningoutput signal from block 508 at block 514 to obtain an overall outputsignal with significantly reduced or removed residual offset, e.g.,according to (1+x)S′−xS″=ΣF[B].

In practice, there are several different ways to implement system 500,which like system 100 of FIG. 1 is a conceptual or generalized depictionof a system and its operation according to an embodiment. In oneembodiment, a first amplifier can be used for the first set of (e.g.,metal) phase signals, and a second amplifier can be used for the secondset of (e.g., polysilicon) phase signals. In another embodiment, thefirst and second sets of phase signals can be multiplexed such that, ina first spinning scheme, the first set of phase signals are amplifiedand processed and, in a second spinning scheme, the second set of phasesignals are amplified by the same amplifier(s). This second embodimentcan be more economical to implement but can be limited by bandwidthrelated to changes in the magnetic field between the first and secondspinning schemes. Nevertheless, at low bandwidths this embodiment can bemore accurate because any amplifier errors are cancelled when the twospinning output signals are combined. Another embodiment of system 500is depicted in FIG. 5B, in which the combined second set of phasesignals (i.e., the output of block 506) is also used to determine theoverall output signal at block 512.

Returning to FIG. 4, FIG. 4B depicts half of the system from FIG. 4Awith a modification of the couplings: instead of connecting both wires404 a, 410 a directly or via tungsten plugs 403 a to the contactdiffusion 406 a of the first sensor device 202, there can also be ashort wire of length d1 between the contact diffusion 406 a and thepoint where both wires are connected together. If d1 is much smallerthan d2, the temperature T11 can be much closer to temperature T1 thanto temperature T′. So the differential input pair of an evaluationcircuit 499 (e.g., a preamplifier in an embodiment) measures a signalproportional to the temperature difference T′−T11, which is close to thetemperature difference T′−T1. It holds that T′−T1=x′*(T′−T11). The samecan be done with the second part of the system labeled with “b” in FIG.4A, such that T′−T2=x′*(T′−T22) holds, whereby T22 is the temperaturewhere wires 410 b and 404 b are shorted. If such a wiring is used inconjunction with FIG. 5A, the output of block 512 would becomexΣk(T₁−T₂)=xx′Σk(T₁₁−T₂₂). This shows that the change of temperaturedifferences T₁−T₂ to T₁₁−T₂₂ means only a small modification of thefactor x to xx′ for the offset compensation. If distance d1 is not smallwith respect to d2, this would lead to a notable degradation in themeasurement of temperature differences because (i) these differencesdecrease, and (ii) the thermal influence of other parts of the system onT₁₁, T₂₂ goes up so that finally they are not any more predominantlydetermined by the contact temperatures T₁, T₂.

In another embodiment, and referring to FIG. 6A, a voltage betweenterminals coupled to a first contact is measured, then a voltage betweenterminals coupled to a second contact is measured. In other words, andreferring to FIG. 6A:V(204a)−V(410a)=k(404a)*(T1−T′)+k(410a)*(T′−T1)V(204b)−V(410b)=k(404b)*(T2−T′)+k(410b)*(T′−T2)If the Seebeck coefficients of interconnects 404 a and 404 b are thesame, and the Seebeck coefficients of wires or terminals 410 a and 410 bare the same, then:V(204a)−V(410a)−(V(204b)−V(410b))=k(404)*(T1−T2)+k(410)*(T2−T1)=(k(404)−k(410))*(T1−T2)In FIG. 6A, regions 408 a and 408 b are portions of different tubs, suchas two contacts, one in each of a first and second tub of a Hall device,though in other embodiments regions 408 a and 408 b can be in differentdevices or can comprise part of something other than a tub within one ordifferent devices. A circuit 401 couples two contacts 405 a and 405 b ofregions 408 a and 408 b in embodiments. Then:V(204a)−V(204b)=k(404a)*(T1−T′)+k(408a)*(T1′−T1)+V(1′1)+V(2′1′)+V(22′)+k(408b)*(T2−T2′)+k(404b)*(T′−T2)V(410a)−V(410b)=k(410a)*(T1−T′)+k(408a)*(T1′−T1)+V(1′1)+V(2′1′)+V(22′)+k(408b)*(T2−T2′)+k(410b)*(T′−T2)→V(204a)−V(204b)−(V(410a)−V(410b))==(k(404a)−k(410a))*(T1−T′)+(k(404b)-k(410b))*(T′−T2)Thereby a voltage drop across circuit 401 was denoted by V(2′1′) and thevoltage drop between 405 a, 406 a by V(1′1) and the voltage drop between406 b, 405 b by V(22′). For k(404 a)−k(410 a)=k(404 b)−k(410 b), weagain obtain V(204 a)−V(204 b)−(V(410 a)−V(410 b), which is proportionalto (T1−T2), such that the temperature difference can be measured by adifference in signals at terminals 410 a, 410 b and 204 a, 204 b.

Referring also to FIG. 6B, another embodiment of system 500 comprisestwo multiplication factors K1 and K2, which can be chosen in order toimplement the same calculations as those illustrated in and discussedwith respect to FIG. 5B. In a simplified depiction, then, and referringto FIG. 6C, block 508 can carry out one or more of the methodologiesdepicted, at least conceptually, as being separate in FIG. 5A, 5B or 6Bin a single calculation circuitry block 508.

Returning briefly to FIG. 2 and the example Hall devices depictedtherein, FIGS. 2E, 2F, 2G and 2H depict four operating phases of a Hallplate 202 having four contacts 1, 2, 3 and 4. Hall plate 202 has90-degree symmetry and is depicted as a simple square with contacts 1-4arranged at four corners, though this can vary in embodiments. In aspinning voltage scheme having four phases 1-4, supply voltage Vs iscoupled to the contact 1-4 having the same phase number, and the contactopposite that contact is coupled to a ground potential. The tworemaining contacts are shorted such that the output signal is equal tothe current flowing between them. For example, in FIG. 2E, phase 1 isdepicted in which contact 1 is coupled to Vs and contact 3 is coupled toa ground potential. An output signal is measured between contacts 2 and4. The output current therefore can be:I _(24,1) =F ₁ [B]+Off₁ +k(T _(2,1) −T _(4,1))+Off_(1,therm)Rotating the coupling arrangement of FIG. 2E by one contact in aclockwise direction in the next three phases provides output signals of:I _(31,2) =F ₂ [B]+Off₂ +k(T _(3,2) −T _(1,2))+Off_(2,therm)I _(42,3) =F ₃ [B]+Off₃ +k(T _(4,3) −T _(2,3))+Off_(3,therm)I _(13,4) =F ₄ [B]+Off₄ +k(T _(1,4) −T _(3,4))+Off_(4,therm)The first element of each equation, e.g., F₂[B], represents a magneticfield dependence, which is assumed but need not be different in eachphase. Off₁, for example represents a resistive offset term for thefirst phase that can depend on an applied potential and is fully definedby an equivalent circuit diagram, e.g., in the form of an asymmetricWheatstone bridge circuit. The term k(T_(2,1)−T_(4,1)), for example,denotes a thermal EMF caused by thermo-coupled contacts, which cancomprise aluminum or polysilicon interconnect lines (refer, for example,to FIG. 4). The final term, Off_(1,therm) denotes a thermal EMF thatoccurs inside an active region of Hall plate 202 due to inhomogeneoustemperature and/or inhomogeneous doping gradients.

The sum of the currents tapped at the metal lines (e.g., terminals 410 aand 410 b in FIG. 4), and for which k≈0 is:

$I_{m} = {{\sum\limits_{j = 1}^{4}\;{F_{j}\lbrack B\rbrack}} + {Off}_{j} + {Off}_{j,{therm}}}$whereas the sum of the currents tapped at the polysilicon lines (e.g.,interconnect lines 404 a and 404 b) is:I _(p) =I _(m) +k(T _(2,1) −T _(4,1) +T _(3,2) −T _(1,2) +T _(4,3) −T_(2,3) +T _(1,4) −T _(3,4))Thus, referring to, e.g., system 500 of FIG. 5A, the following can bedetermined at block 510:I _(p) −I _(m) =k(T _(2,1) −T _(4,1) +T _(3,2) −T _(1,2) +T _(4,3) −T_(2,3) +T _(1,4) −T _(3,4))and it can be used as an input to block 512, which estimates theresidual offset of the spinning voltage Hall plate caused bythermo-voltages

$\sum\limits_{j = 1}^{4}\;{Off}_{j,{therm}}$because there is a strong correlation between

$\sum\limits_{j = 1}^{4}\;{Off}_{j,{therm}}$and (T_(2,1)−T_(4,1)+T_(3,2)−T_(1,2)+T_(4,3)−T_(2,3)+T_(1,4)−T_(3,4)),because the latter is the origin of the former. In this example, thecommon mode potential of the output signals is left free but in otherembodiments can be tied to some predefined potential. Thesemethodologies also can be applied to embodiments in which Hall contactsare used as force-sense contacts, in which the voltage or current at aforce-contact is adjusted until the voltage or current, respectively, ata sense-contact is at some predefined value, such as is disclosed inco-owned U.S. patent application Ser. Nos. 13/022,844 and 13/488,709,which are incorporated herein by reference in their entireties. Thesecontacts can be treated in the same ways as the various contactsdiscussed herein such that temperature sensors can be used to measurethe temperature at each sense-contact, or each sense-contact is coupledto the metal lines and polysilicon interconnect lines discussed hereinwith reference to FIG. 4.

These and other embodiments can also comprise additional features,elements, functions and concepts. For example, systems as discussedherein can further comprise heating elements coupled to the contacts ofa sensor to control the temperatures thereof, based on measurements by atemperature sensor, temperature gradient sensor or temperature sensingcircuitry. Additionally or alternatively in various embodiments, aground reference can be adjusted in order to affect the nonlinearcurrent-voltage characteristic of a device and consequently to control atemperature of one or more contacts. Given that the resistance of a Hallelement generally increases as the reverse bias voltage to itssurroundings (e.g., a surrounding tub, substrate, or shallow tub as atop plate) increases, this effect can be used to control the powerdissipation or the spatial distribution of power dissipation and thusthe temperature distribution of the contacts of the Hall plate.Circumferential isolated structures or elements, such as pn-rings ortrenches, also could be used to implement such a feature in variousembodiments. A control loop can be formed in such a way so as to adjustthe power dissipation or the spatial distribution of power dissipationin the Hall plate until the temperature difference signals of thetemperature gradient sensors are minimized. Thereby, the adjustment canbe frozen during a complete spinning cycle or it can be adjusted betweenoperating phases within a complete spinning cycle.

Another embodiment of a Hall plate 202 is depicted in FIG. 7A andcomprises four contacts C1, C2, C3 and C4 and four temperature sensors,which in this embodiment comprise diodes D1, D2, D3 and D4 but cancomprise other devices or structures in other embodiments. ContactsC1-C4 comprise contact diffusions and are labeled in the same order asin FIGS. 2E-2H herein above. In general, the same or similar referencenumerals will be used herein throughout to refer to the same or similarelements, portions, structures or other features in various drawings. InFIG. 7, a top plate of the Hall effect device is optional and notdepicted.

A terminal t1, t2, t3 and t4 is coupled to each contact, i.e., t1 to C1,t2 to C2, t3 to C3, and t4 to C4. A diode D1-D4 is coupled to eachcontact, i.e., D1 to C1, D2 to C2, D3 to C3, and D4 to C4; and atemperature terminal tt1, tt2, tt3 and tt4 is coupled to each diodeD1-D4, i.e., tt1 to D1, tt2 to D2, tt3 to D3, and tt4 to D4. Inembodiments, each diode D1-D4 is arranged in intimate thermal contactwith its respective contact diffusion C1-C4.

As in other embodiments, a spinning current scheme can be implemented,such that in a first operating phase of a spinning current cycle Hallplate 202 is supplied with current at supply contacts C1, C3, and asignal is tapped at signal terminals C2, C4. More precisely, a supplycurrent IsH is injected into terminal t1 and flows into contact C1,while a second terminal t3 is tied to a reference potential VsL, such asa ground potential or some other suitably chosen potential, and a firstoutput voltage is measured across terminals t2 and t4. In oneembodiment, currents IT2 and IT4 are drawn out of terminals tt2 and tt4,such that:|IT2|+|IT4|<|IsH|In embodiments, IsH is about 10 to about 100 times larger than IT2, andIT2 is equal to IT4. If current IT2 flows over diode D2, a voltage dropoccurs over D2. The same is true for diode D4. Therefore, the voltageacross tt4−tt2 is equal to the voltage across t4−t2 plus the differenceof voltages across temperature device D2 and D4:V(t4)−V(t2)=V(t4)−V(tt4)+V(tt4)−V(tt2)+V(tt2)−V(t2)=V(D4)+V(tt4)−V(tt2)−V(D2)Thus:V(tt4)−V(tt2)=V(t4)−V(t2)+V(D2)−V(D4),whereby the voltage V(D2) is considered to be positive if the anode ofdiode D2 is positive with respect to the cathode, and the same appliesto diode D4. According to one embodiment, then, a first temperatureoutput voltage is measured across terminals tt2 and tt4.

The temperature sensors, which are depicted and described as diodes inFIG. 7A but as previously mentioned can vary in other embodiments, arechosen such that the voltage across each is a strong function oftemperature. Because diodes are known to respond by about −2 mV/° C. totemperature changes, they can be suitable in embodiments. In otherembodiments, however, simple resistors, such as those with a largetemperature coefficient of resistivity, can be used. Low-doped tubs arecommon in integrated circuit technology and have temperaturecoefficients on the order of 5000 ppm/° C.; for voltage drops of about1V across resistors, then, a temperature signal with a sensitivity of1V*5000 ppm/° C.=5 mV/° C. may be achieved. A disadvantage of resistorsas temperature devices, however, is their resistance, which adds to theinternal resistance of Hall plate 202 and increases the noise. Diodes,in contrast, have a much smaller internal resistance which does not addmuch noise to the sensor signals. On the other hand, a resistance couldalso be implemented in layers that are above the silicon substrate andthus above the tub of the Hall effect device. For example, apoly-silicon resistor R1, R2, R3 and R4 placed above the respectivecontacts C1-C4 could be used, and an example of such a configuration isdepicted in FIG. 7B. In general, the temperature device also can be anytwo-pole circuit that has a voltage which depends on temperature and, inembodiments, a low internal resistance. In particular, this circuitcould employ feedback loops to reduce the resistance seen by the outputsignal of the Hall effect device.

FIG. 7C depicts a circuit diagram which illustrates one way in which aspinning current Hall probe 202 is connected to preamplifiers A1 and A2in a first operating phase. Switches S1, S2, S3 and S4 are configured toconnect any of the terminals t1-t4 with any of current source IsH,reference voltage source VsL, and/or inputs of amplifier A1.Analogously, switches ST1-ST4 are configured to connect any of terminalstt1-tt4 with any of the inputs of amplifier A2. Current sources IT1-IT4are configured to be switched on or off during arbitrary operatingphases, whereby the shading of IT1 and IT3 is intended to denote thatIT1 and IT3 may be off during the first operating phase (the onedepicted in this figure and in FIG. 7A). Alternatively, all currentsources IT1-IT4 may be on during all operating phases, which mayminimize errors due to transient effects and/or self-heating. Note thatthe sign of the currents IT1-IT4 may be positive or negative, whichmeans that these currents are either drawn out of Hall device 202(positive) or injected into Hall device 202 (negative). This signchanges the common mode potential at the inputs of amplifiers A1, A2 andmay be chosen appropriately. Amplifier A1 subtracts the two outputsignals at t2 and t4 during the first operating phase and provides aphase signal P1 at its output. Amplifier A2 subtracts two temperatureoutput signals at tt2 and tt4 during the first operating phase andprovides a phase temperature signal PT1 at its output. A2 can beidentical to A1 if A1 is operated in a time multiplexed fashion in oneembodiment.

The voltage across a temperature device (e.g., diodes D1-D4) can varylinearly with temperature (at least in a first order approximation):V(D2)=VT20*(1+ST2*T2)V(D4)=VT40*(1+ST4*T4)where T2 and T4 are the temperatures at contacts C2 and C4, ST2 and ST4are temperature sensitivities, and VT20 and VT40 are the voltages acrossD2 and C4 at zero temperature T2 and T4. If the temperature devices areidentical:VT20=VT40 and ST2=ST4.In most cases, however, the temperature devices have a mismatch:VT20< >VT40 and ST2< >ST4Therefore:V(D2)−V(D4)=VT20−VT40+VT20*ST2*T2−VT40*ST4*T4The difference of voltages across both temperature devices is usuallynot zero, even if the temperatures are identical, i.e., T2=T4.

The system can cope with these errors if it executes a third operatingphase in embodiments in which the sources IsH and VsL are swapped. Thus,in this third operating phase, current source IsH is connected toterminal t3 and reference voltage VsL is connected to t1. Thetemperature devices D1-D4 may be still connected the same way as inoperating phase 1. Then:V′(D2)−V′(D4)=VT20−VT40+VT20*ST2*T2′−VT40*ST4*T4′where the apostrophe or “′” denotes this operating phase. Note that thetemperatures T2′ and T4′ are different than T2 and T4 because the Halldevice is operated with different current direction and due to smallasymmetries and electrical nonlinearity this can lead to slightlydifferent temperatures (e.g., about 0.01° C. in embodiments). The systemcomputes the difference of differential phase temperature signals asfollows:V(D2)−V(D4)−(V′(D2)−V′(D4))=VT20*ST2*(T2−T2′)−VT40*ST4*(T4−T4′)and correlates this with the thermoelectric error of the Hall outputsignals during both operating phases:1^(st) operating phase: V(t4)−V(t2)=S*B+k*(T4−T2)3^(rd) operating phase: V′(t4)−V′(t2)=−S*B+k*(T4′−T2′)whereby resistive offset terms are neglected because they are canceledout in the full spinning current cycle. In the overall spinning currentoutput signal both signals of 1^(st) and 3^(rd) phase are subtracted:V(t4)−V(t2)−(V′(t4)−V′(t2))=2*S*B+k*(T4−T4′−T2+T2′)If the same is done with the phase temperature signals then:V(tt4)−V(tt2)−(V′(tt4)−V′(tt2))=2*S*B+k*(T4−T4′−T2+T2′)+VT20*ST2*(T2−T2′)−VT40*ST4*(T4−T4′)So the phase signals have an error caused by thermo-EMF:k*(T4−T4′−T2+T2′)The phase temperature signals have an extra error caused by thermo-EMF:VT20*ST2*(T2−T2′)−VT40*ST4*(T4−T4′)The system can compare both (e.g. by subtracting them). Thus, the systemcan measure the following:VT20*ST2*(T2−T2′)−VT40*ST4*(T4−T4′)By characterization in the laboratory it is possible to establish atypical relationship between k*(T4−T4′−T2+T2′) andVT20*ST2*(T2−T2′)−VT40*ST4*(T4−T4′). Such a relationship will vary fromdevice to device, from production lot to lot, but it should be stableover the lifetime of a particular device (i.e., as long as VT20*ST2 andVT40*ST4 are stable, which is generally true in practice if stablepn-junctions or stable resistors or other stable devices are used). Thistypical relationship can be used in an algorithm of the sensor system toestimate the termo-EMF-error in the phase signals and finally tocompensate for it (e.g. by subtracting the expected error from the phasesignals).

For example, suppose that there is no mismatch between the twotemperature devices D2 and D4. Then the extra error due to thermo-EMF inthe phase temperature signals isV(tt4)−V(tt2)−V′(tt4)+V′(tt2)−V(t4)+V(t2)+V′(t4)−V′(t2)=VT0*ST*(T2−T2′−T4+T4′)where we used VT0=VT20=VT40 and ST=ST2=ST4. If this is multiplied by anappropriate factor and added to the original phase signals in thespinning scheme, the thermo-EMF of the Hall effect device may becanceled:Vcomp=V(t4)−V(t2)−V′(t4)+V′(t2)−x*{V(tt4)−V(tt2)−V′(tt4)+V′(tt2)−V(t4)+V(t2)+V′(t4)−V′(t2)}=2*S*B+k*(T4−T4′−T2+T2′)−x*VT0*ST*(T2−T2′−T4+T4′)=2*S*Bfork+x*VT0*ST=0orx=−k/(VT0*ST)We call Vcomp the thermo-EMF-compensated signal. This factor x can bedetermined empirically, though an approximation can be determinedtheoretically: If a diode is used as a as temperature device, thenVT0*ST=−2 mV/° C.and k is the Seebeck-coefficient of, e.g., a low n-doped Hall regionwith k=−1500 μV/° C. which givesx=−(−1.5 mV/° C.)/(−2 mV/° C.)=−0.75Thus, the thermo-EMF-compensated signal in the first operating phase isobtained by(1+x)*{V(t4)−V(t2)}−x*{V(tt4)−V(tt2)}and in the third operating phase it is given by(1+x)*{V′(t4)−V′(t2)}−x*{V′(tt4)−V′(tt2)}and in the overall spinning scheme both signals are subtracted.

Thus, the thermo-EMF-compensated signal is a linear combination ofdifferential phase signals (e.g., V(t4)−V(t2)) and differential phasetemperature signals (e.g., V(tt4)−V(tt2)), both of the same phase. Inthe above case, the phase temperature signals are weighted with a factorthat is three times larger than the traditional phase signals:−x/(1+x)=−(−0.75)/(1−0.75)=3. Thus, the dominant part of the signalcomes from the phase temperature signals, with only a minor portion fromthe traditional phase signals, a distinction with respect toconventional approaches. Of course, the weight of differential phasetemperature signals versus differential phase signals depends on thetemperature sensitivity of the temperature sensor. As seen above, thelinear combination is independent on the phase: the same factor x ispresent for first and third phases. The devices D2 and D4, however, areassumed to match perfectly. If other devices D1 and D3 are used in thesecond and fourth phases of a spinning Hall cycle, e.g., according toFIGS. 2E-H and they have different VT0 and ST parameters, this will alsoaffect x. So, generally in so-called orthogonal operating phases, i.e.,phases with different signal contacts (phases 1 and 2 are orthogonal,yet 1 and 3 are not orthogonal), the linear combination for thethermo-EMF-compensated signal is different. Yet in non-orthogonal phasessuch as phases obtained by reversing the polarity of the supply voltageor supply current, the linear combination for the thermo-EMF-compensatedsignal is usually identical.

One basic aspect of various embodiments is that the thermal symmetry ofthe Hall effect device with respect to supply reversal can be optimized.If this is achieved for all systematic effects (like, e.g., geometricsymmetry), there will always be some statistical asymmetries (like,e.g., geometric asymmetries due to manufacturing tolerances), whichcause temperature differences between contacts that should haveidentical temperatures without manufacturing tolerances. Thesetemperature differences can be measured by temperature-differencesensors (i.e., sensors of spatial gradient of temperature) and fromthese measurements corrective values are deduced online that canceloffset caused by thermo-EMFs, if these values are added to (notmultiplied with) the Hall effect signal. This feature of adding theoffset-correction value to the uncompensated signal in order to get thecompensated signal can also be seen in the block diagrams in FIGS. 1,2I, 5A, 5B and 6B. This distinguishes embodiments of offset-compensationfrom conventional temperature compensation approaches which multiply anuncompensated Hall signal by some appropriate function of temperature(i.e., a temperature sensor signal) in order to get a compensated signalwith e.g. temperature independent behavior. These conventionaltemperature compensation systems trim the gain of the system as afunction of temperature, whereas embodiments disclosed herein trim theoffset of the system as a function of temperature gradient.

Now, however, suppose that there is a mismatch between two temperaturedevices D2 and D4. The mismatch can occur in VT20< >VT40 or in ST2<>ST4, or in both. We saw above that the subtraction of signals of firstand third operating phases cancels the VT20 and VT40 terms, which isdesired. Since the extra error due to thermo-EMF in the phasetemperature signals is VT20*ST2*(T2−T2′)−VT40*ST4*(T4−T4′), the systemonly has to deal with mismatches between VT20*ST2< >VT40*ST4. Thus, wecan say VT40*ST4=VT20*ST2*(1−MM), where MM is the mismatch between D2and D4. The extra error due to thermo-EMF in the phase temperaturesignals isVT20*ST2*(T2−T2′)−VT20*ST2*(T4−T4′)*(1−MM)=VT20*ST2*(T2−T2′−T4+T4′)+MM*VT20*ST2*(T4−T4′)Thus, in the presence of mismatch of temperature devices, the systemdoes not measure T2−T2′−T4+T4′, but rather:T2−T2′−T4+T4′+MM*(T4−T4′)Consequently, the error is moderate as long as T4−T4′ is similar toT2−T2′−T4+T4′. The error is large, however, when|T4−T4′|>>|T2−T2′−T4+T4′|. In other words: The fluctuation oftemperature at an output contact in two operating phases with reversedsupply voltage or current should not be large against the fluctuation oftemperature difference between both output contacts in these operatingphases. This means that the total power dissipation in the Hall effectdevice should change as little as possible when the supply is reversed.It also means that the power density near the output contacts shouldremain as constant as possible when the supply is reversed. Therefore,the operating conditions should be such that the common-mode potentialsat the output contacts should remain identical or nearly so when supplyis reversed in embodiments.

This is illustrated, for example, in FIGS. 7D and 7E. FIG. 7D depicts aHall plate 202 with four contacts C1-C4, which is biased in anundesirable way because the common mode potential (0.5*V(C2)+0.5*V(C4))changes when the supply voltage is reversed due to the electricalnonlinearity of the Hall effect device. The common mode output voltageis slightly below half of the supply voltage due to electricalnonlinearity of the device. Thus, it is about 0.45*V(C1) in the firstoperating phase and 0.45*V′(C3) in the third operating phase. Assuming aperfectly symmetric Hall effect device, then V(C1)=V′(C3), i.e., thesupply voltage is identical if the supply currents are identical butwith different polarities. The common mode output voltages also areidentical in both phases, and consequently the temperature T2 should bevery similar to T2′ (and also T4 should be similar to T4′). Yet if theHall effect device is slightly asymmetrical such that contact C1 is,e.g., about 1% smaller than C3, this will lead to V(C1) being differentfrom V′(C3), and then also the common mode output voltages in bothphases are different. Additionally, the temperatures T2 and T2′ (or T4and T4′) should differ significantly more than before.

FIG. 7E shows the same device biased in a more advantageous way, whereinthe common mode potential is controlled to be at the same level when thesupply is reversed. The operational amplifier OPA compares the referencevoltage Vref with the sum V(C2)+V(C4). If the sum is the larger of thetwo, the output of op-amp OPA goes up, which pulls the gate of the NMOSup such that the NMOS sinks more current, which in turn pulls V(C2) andV(C4) down. Thus the common mode is controlled to a value of Vref/2.

There are numerous other ways to keep the common mode potential at fixedvalues during parts of the spinning Hall scheme, and the examplesdiscussed herein are not limiting. Many of these schemes areadvantageous because they reduce the matching requirements for thetemperature devices, e.g., diodes D2 and D4. A goal, generally, is tokeep the common mode potential of the output constant when the supply isreversed, though the differential potential V(C2)−V(C4) is still free tooutput the magnetic field signal. If the common mode potential isconstant, the power density and thus the temperature distribution alsoshould be constant. Note that the common mode potential can have variouskinds of influences on the Hall region: if the Hall region is isolatedagainst the environment by a reverse biased pn-junction, as is typical,the common mode potential determines the reverse bias and thisdetermines the width of the depletion layer, which defines the activewidth of the Hall region. The thinner the active Hall region, the higherits resistance will be. On the other hand, the common mode potential mayaffect the number of free charges in the active Hall region or at leastin parts of it (e.g., through charge accumulation effects), and thisalso affects the resistance. The resistance also affects the powerdissipation and thus the temperature distribution in the device.

In embodiments, the system estimates T2−T4−T2′+T4′, as was illustratedin the discussion herein above of the simple case with perfect matching.Mismatch will lead to reduced accuracy in this estimation, but a levelof accuracy that is desired or required can vary. In embodiments, thetemperature differences T2−T4 in differential outputs of Hall effectdevices as low as about 0.001° C. can be estimated. This provides athermo-EMF-voltage of about 1.5 μV for a Seebeck coefficient of 1500μV/° C. A typical Hall effect device has a magnetic sensitivity of about50 mV/T when operated at a 1V supply, such that 1.5 μV corresponds to a30 μT offset. This offset occurs at all phases of a spinning Hall probe,and it is stochastic, whereby the offsets in orthogonal phases arepresumably statistically independent and also in the non-orthogonalphases should be basically independent. Thus, if a spinning scheme has 4operating phases, the residual offset should be about sqrt(4), or 2times lower. This gives a residual offset of about 15 μT, whichgenerally corresponds with observations by the inventor in thelaboratory.

When a Hall effect device is operated in a spinning Hall scheme, thetemperature will also vary with each new operating phase. Moreover, thesystem has a certain latency due to the thermal mass of the circuitdevices, and this can lead to the temperature in the n-th operatingphase also being influenced to a certain degree by the temperatureduring the (n−1)-th or, in general, any of the preceding operatingphases. Referring again to FIG. 2E, which shows a Hall effect deviceoperated in a first phase, the contact at highest potential (C1) willalso attain the highest temperature due to the electrical nonlinearityof the device, whereas the grounded contact C3 has the lowesttemperature. If the second operating phase shown in FIG. 2F followsshortly after the first one, contacts C1 and C3 changed roles: in phase1 each was a supply contact, whereas in phase 2 each is now a signalcontact. As C1 was slightly warmer than C3, this gives a temperaturedifference between these two output contacts in the start of phase 2.Consequently, it also provides a thermo-EMF voltage, which causes anoffset error. If phase 2 lasts notably longer than the thermal timeconstant of the Hall effect device, contacts C1 and C3 willeventually—at the end of phase 2—be at identical temperatures, ifperfect symmetry of the device is assumed. Thus, a transient temperaturedifference between the output contacts can occur so that it changesduring a phase, and the duration of the operating phase can have asignificant impact on these effects: if the spinning Hall scheme isexecuted very slowly these transient effects may be ignored, yet, if itis executed very fast the temperature during an operating phase may bepredominantly determined by prior operating phases and only to anegligible extent by the current operating phase. Moreover, the systemmeasures Hall signals and temperature differences synchronously: atevery point in time, when the Hall signal is measured the thermo-EMFerror is part of this Hall signal and therefore the system should knowthe temperature differences at the output contacts for these points intime, too.

Here, however, two types of systems may be distinguished: integratingsystems and sampled systems. An integrating system such as, e.g., acontinuous time sigma-delta analog-to-digital converter (CT-SD-ADC)integrates the Hall output signal during a certain time interval, e.g.,during the entire operating phase. In such a case the system can alsointegrate the temperature-difference between the output contactssynchronously. Alternatively, a successive approximationanalog-to-digital converter (SAR-ADC) usually samples the Hall signal,which means it freezes the value using a sample-and-hold technique andthen converts this static value. In this case also the temperaturedifference of the output contacts can be sampled at the same time theHall signal is sampled.

Under static conditions the temperature distribution in a 100 μm×100μm-square silicon Hall plate with 5 μm thickness and typicalnonlinearity, operated at 3V supply in phase 4 of FIG. 2H, is depictedin FIG. 8A. As can be seen, contact C4 is at highest potential and alsoat highest temperature, about 0.062° C. above a room temperature of 300K.

FIG. 8B depicts the transient temperature behavior of several points inHall plate 202 of FIG. 8A during a spinning Hall cycle. The pulse-shapedcurves denote temperatures of the four contacts, whereas the smoothcurve is the temperature in the center of Hall device 202 (e.g., activearea 226). In this embodiment, each operating phase is about 10 μs long,and there is 300 K initially before the device is powered up. Thus, fastthermal time constants of about 1-2 μs can be seen. Two different pulse“teeth” in each operating phase are also present, which is the high andlow potential supply contacts, and two equal “valleys,” which are theoutput contacts. The temperature difference between supply and signalcontacts is about 0.03° C., whereas the temperature difference betweenboth supply contacts is less than about 0.001° C.

If the initial mismatch between diodes D2-D4 is too large, the systemcan perform an auto-calibration in embodiments. In one embodiment,therefore, a heating element can be used which is designed in such a wayas to generate the same temperature on D2 and D4. This heating elementcan be activated for a certain period of time and then the output ofD2-D4 measured (i.e., either once in an end-of-line calibration, orduring power-up of the sensor system, or repeatedly, e.g., every 100ms). If the output changes when the heating element is activated, thischange is stored and subsequently subtracted from each measurement andused for correction of subsequent measurements.

For example, if the heating element is off, voltages across thetemperature diodes D2-D4 are V(D2), V(D4) and the temperatures at thediodes are T2, T4, respectively. If the heating element is on, thevoltages are V″(D2), V″(D4) with temperatures T2+dT and T4+dT,respectively. The system can measure these voltages and compute(V(D2)−V(D4)−V″(D2)+V″(D4))/(V(D2)−V″(D2)), which is equal to1+VT40*ST4/(VT20*ST2), which gives the mismatch of temperaturesensitivities of both temperature sensors.

Alternatively, some parameter of one or both of diodes D2 or D4 can beadjusted to reduce the observed change in D2-D4-output to zero. Forexample, if D2 and D4 are diodes or resistors, as discussed above, thesystem could change the current IT2 through D2 until the temperaturedifference observed at D2-D4 does not depend on the heating elementbeing on or off. This procedure can trim the sensitivity of D2 to matchD4. Even though the change in IT2 also changes the self-heating of thetemperature sensor, this generally has no adverse effect on the systemas long as this self-heating is the same during on- and off-times of theheater.

Note that usually there are different temperatures at D2 and D4 due tooperation of the Hall effect device or other heat sources present in thesystem. Therefore, the system can extract only the difference intemperature difference between heating element on and off, so only thesuperimposed temperature difference caused by the symmetric heatingelement is relevant. The heating element for auto-calibration should beperfectly symmetric with respect to both temperature sensors D2 and D4(and for orthogonal phases either the same or a different heatingelement needs to be perfectly symmetric to D1 and D3) in embodiments sothat it generates the same temperature increase at D2 and D4 (up tobetter than 1%, such as 0.1% or even better, if possible, inembodiments). There are several approaches which can be used to achievethis: for example, either one heating element is placed symmetricallywith respect to both temperature sensors D2 and D4 (or other diodes ortemperature sensing devices, as the case may be in any particularembodiment or configuration, with the examples here relating thedepiction in the drawings for convenience only), or each temperaturesensor has its own dedicated heating element. In the second case theheating elements should match perfectly, such that now it can be seenthat the problem of mismatch has merely been shifted from D2-D4themselves to their respective heating elements. This still may be aviable option, however, if the mismatch of the heating elements is lessthan the mismatch of the temperature devices. Even in this case it canbe beneficial to make the spacing between temperature sensor andrespective heating element sufficient as every small change in layerthickness or other details may have a large effect on the temperatureexcursion on the temperature sensor caused by the heater.

For example, suppose both D2 and D4 are diodes and have heating elementsHT2 and HT4, which comprise resistive strips placed above them.Resistive strips and this particular placement are but one example ofsuitable heating elements and arrangement. Even if HT2 and HT4 matchperfectly, it is likely that the thickness of an intermetal dielectricor some other structure between HT2 and D2 differs by, e.g., 1% from thesame structure between HT4 and D4. This is all the more likely since thevertical spacing between HT2 and D2 is only about 1 μm or similar.Although HT2 generates the same heat and heat density as HT4, thetemperatures at D2 and D4 would differ. The situation improves, however,if the spacing between D2 and HT2, and also between D4 and HT4, isincreased, e.g., by a lateral distance of about 10 μm. Then the thermalcoupling is less intimate but more stable against production tolerances.On the other hand, the larger the distance between D2 and HT2, thelarger the influence the surrounding area and structures arranged therecan have on the thermal coupling between them. Therefore, it can beadvantageous for the layout of other circuit devices around D2-HT2 andD4-HT4 to be symmetrical in order to have exactly the same thermalcoupling between D2-HT2 and D4-HT4. The same holds if only a singleheating element is used for both D2 and D4; then the mismatch betweenHT2 and HT4 is avoided. Of course, it is typically impractical inpractice to have the layout of the entire system symmetrical withrespect to the heating element and all temperature sensors D1-D4. Thus,in embodiments, it can be made symmetric within a certain distance,whereas at large distances the symmetry can be imperfect so long as thecoupling of the heat source and temperature sensors is still strongenough. With the above given numbers one can estimate if a certainasymmetry is still acceptable: If the mismatch should be reduced toabout 0.1% due to auto-calibration, the thermal coupling between theheating element and D1-D4 must match at least up to about 0.1%. Anyasymmetry can be modelled in a numerical computer code (e.g., a finiteelement simulation) and the thermal coupling can be studied.

If the main sensor has contact diffusions of a first conductivity type(e.g., a Hall sensor has n-doped contact diffusions), then it may bepossible to place smaller diffusion tubs of a second, oppositeconductivity type within the contact diffusions of the firstconductivity type. In the case of the Hall sensor this would be smallerp-tubs within n-tubs. This gives pn-junctions which could be used astemperature device of this respective contact. One example is depictedin FIG. 9, which is a version of FIG. 3 discussed above. Such aconfiguration can save space and make the thermal coupling betweencontacts and temperature sensors more intimate. In an embodiment,contact 204 a can be ring-shaped, completely encircling tub 306 whenviewed from the top (as opposed to the side cross-sectional view of FIG.9) so that the current flowing into/out of the temperature device doesnot affect the potential distribution in the main sensor. Note that FIG.9 is a schematic view of a single contact having an integratedpn-temperature diode; in practice, Hall-effect devices such as Hallplates or vertical Hall-effect devices typically have three or morecontacts each having such a pn-junction. In general, all contacts whichare used to tap a signal in at least one phase of a spinning Hall schemeshould have such a pn-junction.

Thus, various embodiments of sensors, systems and methods forcompensating for the effects of thermal EMF have been discussed herein,with reference to several example embodiments and depictions that arenot limiting to the overall concepts. For example, which examplesrelated to Hall effect sensors have been discussed, other sensor typescan be used, including other magnetic field sensors, mechanical stresssensors, and others. In general, however, the residual offset can becorrelated to temperature fluctuations at sensor contacts, which can inturn be correlated with thermal EMFs, and residual offset can be reducedor eliminated by adding a correction term or compensation signal, or byimplementing a control loop, based on sensed temperatures at one or moresensor contacts.

Various embodiments of systems, devices and methods have been describedherein. These embodiments are given only by way of example and are notintended to limit the scope of the invention. It should be appreciated,moreover, that the various features of the embodiments that have beendescribed may be combined in various ways to produce numerous additionalembodiments. Moreover, while various materials, dimensions, shapes,configurations and locations, etc. have been described for use withdisclosed embodiments, others besides those disclosed may be utilizedwithout exceeding the scope of the invention.

Persons of ordinary skill in the relevant arts will recognize that theinvention may comprise fewer features than illustrated in any individualembodiment described above. The embodiments described herein are notmeant to be an exhaustive presentation of the ways in which the variousfeatures of the invention may be combined. Accordingly, the embodimentsare not mutually exclusive combinations of features; rather, theinvention can comprise a combination of different individual featuresselected from different individual embodiments, as understood by personsof ordinary skill in the art. Moreover, elements described with respectto one embodiment can be implemented in other embodiments even when notdescribed in such embodiments unless otherwise noted. Although adependent claim may refer in the claims to a specific combination withone or more other claims, other embodiments can also include acombination of the dependent claim with the subject matter of each otherdependent claim or a combination of one or more features with otherdependent or independent claims. Such combinations are proposed hereinunless it is stated that a specific combination is not intended.Furthermore, it is intended also to include features of a claim in anyother independent claim even if this claim is not directly madedependent to the independent claim.

Any incorporation by reference of documents above is limited such thatno subject matter is incorporated that is contrary to the explicitdisclosure herein. Any incorporation by reference of documents above isfurther limited such that no claims included in the documents areincorporated by reference herein. Any incorporation by reference ofdocuments above is yet further limited such that any definitionsprovided in the documents are not incorporated by reference hereinunless expressly included herein.

For purposes of interpreting the claims for the present invention, it isexpressly intended that the provisions of Section 112, sixth paragraphof 35 U.S.C. are not to be invoked unless the specific terms “means for”or “step for” are recited in a claim.

What is claimed is:
 1. A sensor system comprising: a first sensorelement arranged on a substrate and configured to sense a physicalquantity in at least one operating phase; a second sensor elementarranged thermally proximate the first sensor element on the substrateand configured to sense a spatial gradient of temperature within thefirst sensor element during at least a portion of the at least oneoperating phase; and circuitry coupled to the first sensor element andthe second sensor element via contacts on the substrate and configuredto combine a signal of the first sensor element related to the sensedphysical quantity with a signal of the second sensor element related tothe sensed spatial gradient of temperature sampled during the sameportion of the at least one operating phase to obtain an output signalindicative of the physical quantity.
 2. The sensor system of claim 1,wherein the at least one operating phase comprises a spinning schemecomprising at least two operating phases, wherein the first sensorelement is configured to be operated in the spinning scheme comprisingat least two operating phases, wherein a spatial distribution of currentin the first sensor element is different in each of the at least twooperating phases, and wherein the second sensor element is configured tosense the spatial gradient of temperature within the first sensorelement when the first sensor element senses the physical quantity inthe at least two operating phases.
 3. The sensor system of claim 2,wherein the first sensor element comprises at least three terminals,wherein different ones of the plurality of terminals comprise a signalterminal in the at least two operating phases.
 4. The sensor system ofclaim 1, wherein the second sensor element is coupled to the main sensorelement.
 5. The sensor system of claim 1, wherein the first sensorelement comprises a Hall-effect sensor element, and the second sensorelement comprises a temperature sensor element.
 6. The sensor system ofclaim 5, wherein the Hall-effect sensor element comprises a Hall plate.7. The sensor system of claim 5, wherein the Hall-effect sensor elementcomprises a vertical Hall-effect sensor element.
 8. The sensor system ofclaim 1, wherein the spatial gradient of temperature is a temperaturedifference between an output contact of the first sensor element and areference point.
 9. The sensor system of claim 1, wherein the secondsensor element comprises a first temperature sensor element and a secondtemperature sensor element each coupled to the first sensor element tosense a spatial gradient of temperature therein.
 10. The sensor systemof claim 9, wherein a thermal coupling of the first temperature sensorelement to a first output contact of the first sensor element isstronger than a thermal coupling of the first temperature sensor elementto a second output contact of the first sensor element, and wherein athermal coupling of the second temperature sensor element to the secondoutput contact of the first temperature sensor element is stronger thana thermal coupling of the second temperature sensor element to the firstoutput contact of the first temperature sensor element.
 11. The sensorsystem of claim 9, wherein first sensor element, the first temperaturesensor element and the second temperature sensor element are disposed ona surface of the substrate.
 12. The sensor system of claim 1, whereinthe second sensor element is configured to sense a spatial gradient oftemperature related to at least one contact of the first sensor element.13. The sensor system of claim 1, wherein the circuitry is configured tocombine the signal of the first sensor element with the signal of thesecond sensor element to obtain an output signal indicative of thephysical quantity, and wherein the output signal is compensated for athermal electromotive force (EMF) affecting the first sensor element.14. A method comprising: obtaining a first signal by sensing a firstphysical quantity in at least one operating phase by a first sensor;obtaining a second signal by sensing a spatial gradient of temperatureof the first sensor during a portion of the at least one operating phasewhen the first physical quantity is sensed; and reducing an offset errorin the first signal by combining the first and second signals from theat least one operating phase.